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The team also announced that linebacker David Harris signed his one-year tender offer.

Taylor compiled 36 tackles and five sacks last season for the Jets, his lone campaign with the team. The 36-year-old spent the first 11 seasons of his career with Miami before joining the Redskins for the 2008 season. He then returned to the Dolphins in 2009 before joining their AFC East rivals.

The Akron product has totaled 560 tackles, 132 1/2 sacks and eight interceptions, including three returned for scores, during his career.

Jenkins recorded only one tackle in the season opener against Baltimore before tearing his left anterior cruciate ligament and missing the remainder of the campaign. He suffered the same injury in 2009 that limited him to six games.

The 31-year-old has recorded 279 tackles and 24 sacks in his 10 years in the league with Carolina and the Jets.

Woody suffered a season-ending Achilles injury in New York's AFC Wild Card win over the Indianapolis Colts. The 33-year-old Woody, who also had stints with the Patriots and Lions, has started in 166 of the 173 games he has appeared in during his career.

Harris was given the franchise tag last month after registering 99 tackles and three sacks in 2010. He has compiled 428 stops, 14 1/2 sacks and two interceptions during his four seasons in the NFL, all with New York.